Explicit Construction On Three Types Of Special Surfaces

This paper includes two chapters.In Chapter one, we construct Lagrangian surfaces in CP~2 and CH~2 by using Legendre curves in the 3-sphere and anti de Sitter 3-space. Among these surfaces, we characterize minimal surfaces in terms of the properties of the curvatures of the generating curves.In Chapter two, we investigate some surfaces with constant Gauss curvature in hyperbolic space H~3(—1). First, we construct a class of noncongruent surfaces with constant Gauss curvatures in hyperbolic space H~3(—1), and principal curvatures of these surfaces are all bounded; then we give a type of isometric immersions from H~2(c)(—1 < c < 0) into H~3(—1), and these immersions have unbounded principal curvatures.